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## 13 January 2015

### Mail Time: How do you convince a student that motion is not always in the direction of the larger force?

Two identical blocks of mass m are connected by a string over a pulley.  Block A is on a horizontal, frictionless surface; Block B hangs from the string. Consider now that, having previously been given a brief initial shove, block A is sliding to the left across the smooth tabletop.

•Is the tension in the rope greater than, less than, or equal to mg?

One of a reader's students asked, "Why is the tension less than mg if the block is sliding left?"

She continued... "How can it slide left and the tension not be greater than mg if the block is pulled up even if it is slowing down?"

The reader explained that block A's acceleration and net force are to the right, since the system will slow down after the initial push. If tension is greater than mg then block B would have an upward acceleration, which would mean that the block would speed up while moving upward -- that doesn't happen.  And finally, the FBD  shows the block on top with only one force, that being to the right -- rightward net force on Block A requires a downward net force on Block B.

She wasn't satisfied with these explanations. Is there a better way of putting it?

I wouldn't say I have any better ways of explaining this issue; I use all of the above explanations.  This student is still conflating force and motion.  Any object -- not just these blocks -- can move opposite the direction of the net force acting on it.  That just means the object is slowing down.

Ask her and the class for examples of objects that move in one direction while experiencing a net force in the other direction.  A ball moving up in free-fall is the canonical example.

I'd then set up this described system* in class, using a force probe or a spring scale to measure the tension in the string.  It's fun to watch the spring scale reading dip below the weight of the hanging mass as soon as you let go.  If your class is too large for all to watch the spring scale dial, use the Vernier force probe and project its reading on the screen.

* It's often called the "modified atwood" when two block are connected by a string over a pulley, but one of the blocks is on a horizontal surface.  See AP Physics B 2012 exam problem 1.

I ain't saying this experiment will solve all your student's misconceptions, but it should at least stop her from arguing.  That's what I love about physics: my students can argue, sure, until a smiley but facetious "Bet you \$100 that the experiment works the way I say it will?" shuts them up a treat.  :-)